Atomic and molecular decomposition of homogeneous spaces of distributions associated to non-negative self-adjoint operators

Athanasios Georgiadis, Gerard Kerkyacharian, George Kyriazis, Pencho Petrushev

Research output: Working paperResearch

Abstract

We deal with homogeneous Besov and Triebel-Lizorkin spaces in the setting of a doubling metric measure space in the presence of a non-negative self-adjoint operator whose heat kernel has Gaussian localization and the Markov property. The class of almost diagonal operators on the associated sequence spaces is developed and it is shown that this class is an algebra. The boundedness of almost diagonal operators is utilized for establishing smooth molecular and atomic decompositions for the above homogeneous Besov and Triebel-Lizorkin spaces. Spectral multipliers for these spaces are established as well.
Original languageEnglish
PublisherArXiv
Number of pages41
Publication statusPublished - 2018

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Triebel-Lizorkin Space
Homogeneous Space
Self-adjoint Operator
Non-negative
Atomic Decomposition
Decompose
Metric Measure Space
Markov Property
Sequence Space
Heat Kernel
Doubling
Operator
Multiplier
Boundedness
Algebra
Class

Cite this

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abstract = "We deal with homogeneous Besov and Triebel-Lizorkin spaces in the setting of a doubling metric measure space in the presence of a non-negative self-adjoint operator whose heat kernel has Gaussian localization and the Markov property. The class of almost diagonal operators on the associated sequence spaces is developed and it is shown that this class is an algebra. The boundedness of almost diagonal operators is utilized for establishing smooth molecular and atomic decompositions for the above homogeneous Besov and Triebel-Lizorkin spaces. Spectral multipliers for these spaces are established as well.",
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Atomic and molecular decomposition of homogeneous spaces of distributions associated to non-negative self-adjoint operators. / Georgiadis, Athanasios; Kerkyacharian, Gerard; Kyriazis, George ; Petrushev, Pencho.

ArXiv, 2018.

Research output: Working paperResearch

TY - UNPB

T1 - Atomic and molecular decomposition of homogeneous spaces of distributions associated to non-negative self-adjoint operators

AU - Georgiadis, Athanasios

AU - Kerkyacharian, Gerard

AU - Kyriazis, George

AU - Petrushev, Pencho

PY - 2018

Y1 - 2018

N2 - We deal with homogeneous Besov and Triebel-Lizorkin spaces in the setting of a doubling metric measure space in the presence of a non-negative self-adjoint operator whose heat kernel has Gaussian localization and the Markov property. The class of almost diagonal operators on the associated sequence spaces is developed and it is shown that this class is an algebra. The boundedness of almost diagonal operators is utilized for establishing smooth molecular and atomic decompositions for the above homogeneous Besov and Triebel-Lizorkin spaces. Spectral multipliers for these spaces are established as well.

AB - We deal with homogeneous Besov and Triebel-Lizorkin spaces in the setting of a doubling metric measure space in the presence of a non-negative self-adjoint operator whose heat kernel has Gaussian localization and the Markov property. The class of almost diagonal operators on the associated sequence spaces is developed and it is shown that this class is an algebra. The boundedness of almost diagonal operators is utilized for establishing smooth molecular and atomic decompositions for the above homogeneous Besov and Triebel-Lizorkin spaces. Spectral multipliers for these spaces are established as well.

M3 - Working paper

BT - Atomic and molecular decomposition of homogeneous spaces of distributions associated to non-negative self-adjoint operators

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